Interactions Hubbard model

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

Many electron systems such as molecules and quantum dots show the complex phenomena of electron correlation caused by Coulomb interactions. These phenomena can be described to some extent by the Hubbard model [76]. This is a simple model that captures the main physics of the problem and admits an exact solution in some special cases [77]. To calculate the entanglement for electrons described by this model, we will use Zanardi s measure, which is given in Fock space as the von Neumann entropy [78]. 

Schematic diagrams appropriate to NMP/TCNQ and TTF/TCNQ are shown in Fig. 30 and are based on experimental studies. Application of the one-dimensional Hubbard model to analyse low and high temperature data for NMP/TCNQ yielded consistent values of U and t. For TTF/TCNQ and HMTSF/TCNQ, the increased cation polarizability is believed to have successfully reduced the strength of the effective electron-electron interaction with the result that a true metal-semiconductor transition is observed at 58 K for TTF/TCNQ which disappears completely for HMTSF/TCNQ. At present the advantages of using complex salts as against simple salts of charge-transfer systems to produce organic metals are not clear, particularly since the...

The main equation for the d-electron GF in PAM coincides with the equation for the Hubbard model if the hopping matrix elements t, ) in the Hubbard model are replaced by the effective ones Athat are V2 and depend on frequency. By iteration of this equation with respect to Aij(u>) one can construct a perturbation theory near the atomic limit. A singular term in the expansions, describing the interaction of d-electrons with spin fluctuations, was found. This term leads to a resonance peak near the Fermi-level with a width of the order of the Kondo temperature. The dynamical spin susceptibility in the paramagnetic phase in the hydrodynamic limit was also calculated. 

Finally, for purposes of comparison, it is useful to have a pi electron model which makes neither the Hiickel nor the VB assumptions about the strength of the electron-electron interaction. Such a model can provide a smooth bridge between the Hiickel and Heisenberg models as the relative strength of the chemical bonding and electron repulsion interactions between electrons are changed. Such a role is played by the Pariser-Parr-Pople (PPP) model [21,22], and its close relative, die Hubbard model [23], The PPP model can be... 

The exact FCI (frill configuration interaction) solution of the PPP or Hubbard model is possible for molecules with up to about 16 atoms in the pi system. Any of the standard methods for performing approximate ab initio calculations, such as limited configuration interaction, Moeller-Plesset perturbation theory, or coupled cluster theory, may be applied to these models as well. All are expected to be very accurate at low order when U is small, but all will have to be pushed to higher order as U increases. 

The neutral-ionic transition (NIT) at t = 0 occurs abruptly[94] when the Madelung energy M of the ionic lattice exceeds the energy I — A to transfer an electron form D to A. Long-range Coulomb interactions are treated self-consistently as part of A in the modified Hubbard model[95],... 

As a result we have obtained the effective Hamiltonian with the two types of interaction of neighboring segments. The competition between these types of interactions leads to the formation of a magnetic polaron similar to the anisotropic one band U=oo Hubbard model. 

---